Fig. 1
From: A topological data analysis based classification method for multiple measurements
Five datapoints in two-dimensional space and the associated simplicial complex. The full simplicial complex is the purple 2-simplex and the three connected 1-simplices drawn here dashed. The boundary matrices are ∂1 and ∂2. Homology of this complex in degree 0 is 1 saying that there is one connected component. Homology in degree 1 is 1 indicating the loop created by the dashed 1-simplices